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F(x) = x^2– 2x + 3; f(x) = –2x + 12

User Ekeren
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2 Answers

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Answer:

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User Venita
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Final Answer:

The values of x that satisfy the system f(x) = x^2 - 2x + 3 = -2x + 12 are x = 3 and x = -3.

Step-by-step explanation:

Step 1: Set the functions equal:

f(x) = x^2 - 2x + 3

f(x) = -2x + 12

Setting them equal:

x^2 - 2x + 3 = -2x + 12

Step 2: Combine like terms:

Move all x terms to one side:

x^2 - 2x + 2x = 12 - 3

Simplify:

x^2 = 9

Step 3: Solve the quadratic equation:

Take the square root of both sides (remembering to consider both positive and negative square roots):

√(x^2) = ±√9

x = ±3

Therefore, the values of x that make the two functions equal are x = 3 and x = -3.

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Complete Question

Consider the functions f(x) = x^2 - 2x + 3 and f(x) = -2x + 12.

Solve the quadratic equation to find the values of x that satisfy the given system.

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User Cuper Hector
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